Question

IQ is normally distributed with a mean of 100 and a standard deviation of 15. Suppose one individual is randomly chosen. Let X = IQ of an individual. The middle 30% of IQs fall between what two values?

P(x₁ < X < x₂) = .3

State the two values. (Round your answers to the nearest whole number.)

Answer 1

P(X < X1) = 0.35

Or, P((X - )/ < (X1 - )/) = 0.35

Or, P(Z < (X1 - 100)/15) = 0.35

Or, (X1 - 100)/15 = -0.39

Or, X1 = -0.39 * 15 + 100

Or, X1 = 94.15 = 94

P(X > X2) = 0.35

Or, P((X - )/ > (X2 - )/) = 0.35

Or, P(Z > (X2 - 100)/15) = 0.35

Or, P(Z < (X2 - 100)/15) = 0.65

Or, (X2 - 100)/15 = 0.39

Or, X2 = 0.39 * 15 + 100

Or, X2 = 105.85 = 106